In this paper a parallel algorithm is developed for Hermite Interpolation k-ary n-cube network. The algorithm involves three phases: initial phase; main phase and final phase. The computational statistics for the parallel algorithm are also discussed. For N = k points Hermite Interpolation the parallel algorithm in worst case involves N/2 data communications, 2N+6 multiplications , 2N+3 subtrac...

Abstract. It is shown that an appropriate combination of methods, relevant to operational calculus and to special functions, can be a very useful tool to establish and treat a new class of Hermite and Konhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Hermite and Konhauser polynomials and discuss the links w...

Hermite and Smith normal form are important forms of matrices used in linear algebra. These terms have many applications in group theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Hermite and Smith normal form of large dense matrices. The main problems of the c...

An interesting property of the midpoint rule and trapezoidal rule, which is expressed by the so-called Hermite–Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite–Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. I...

Utilizing early time response and low-frequency data, the complete electromagnetic response of a threedimensional conducting structure is generated. By using mutually complementary data, simultaneous extrapolation in time and frequency domains are carried out. This is performed through the use of the associated Hermite polynomials. The interesting property of the Hermite polynomials is that the...

This paper introduces a new test statistic of Normality which evaluates the cross covariances between choosen Hermite polynomials which are zero under the null hypothesis. The special form of the test leads to a modi ed sphericity statistic and we have called it Hermite Normality Test (SH). We present brie y its asymptotical distribution both under the null and nonnull hypothesis. Large simulat...

A numerical method for a class of forward-backward stochastic differential equations (FBSDEs) is proposed and analyzed. The method is designed around the Four Step Scheme (Douglas-Ma-Protter, 1996) but with a Hermite-spectral method to approximate the solution to the decoupled quasilinear PDE on the whole space. A rigorous synthetic error analysis is carried out for a fully discretized scheme, ...

A hierarchical Hermite WENO reconstruction-based discontinuous Galerkin method, designed not only to enhance the accuracy of discontinuous Galerkin method but also to avoid spurious oscillation in the vicinity of discontinuities, is developed for compressible flows on tetrahedral grids. In this method, a quadratic polynomial solution is first reconstructed from the underlying linear polynomial ...

We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected complete matchings, oscillating tableaux, and rooted maps and show weight-preserving bijections between these objects. Several identities, linearization form...

We study the structure of solutions of the one-dimensional non-linear pseudodifferential equation describing the dynamics of the p-adic open string for the scalar tachyon field p 1 2 ∂ t Φ = Φ. We elicit the role of real zeros of the entire function Φ(z) and the behaviour of solutions Φ(t) in the neighbourhood of these zeros. We point out that discontinuous solutions can appear if p is even. We...